Ring Profile (Circle Average) (also see diffraction ring example).

This tool a subset of the Electron Diffraction Tools and is for plotting a 'radial' average of a circular symmetric pattern. It is accessed via the EDIF buttons window made using the More Buttons... EDIF Tools button.. Image files are loaded via the MLx > Image Files menu. Other image processing functions, such as black/white inversion are done with the Image - Buttons.

Instructions for taking a ring profile.

Load the image with the MLx > Image Files > Tiff > Read menu or as appropriate.
If necessary, invert the pixel values with the Adjust...Invert_pixel_values button.
Click the -> ring window button.

Other relevant buttons:

Help Shows this page.
Plot - Ring window Plots the circle average once the ring is centered on the image pattern.
Plot - Other Im Plots the circle average for another (gray level) image window of the same size as the ring window for which the circle has already been centered.
Save Profile Saves the a circle average profile (of the top proile plot window) to a disk file.
Print Parameters Prints the coordinates of the circle center and other information to the Monitor or Listener window.
Set Center Once the ring has been initialized with the -> R Window button, the center can be set manually with this menu. Values from previously centered images may be read and copied using the Print Parameters menu. Normally the center will be set using the mouse as shown below.

Make the ring tool visible with the Show Button.
This is a SIMS image of the cross section of a fiber optic.
Move the ring to the center of the pattern as shown here. Do this by 'mousing' the small central circle. The two smaller circles on the periphery are for changing the radius of the circle and the missing arc gap (which is useful for analyzing electron diffraction images where the beam stop obstructs part of the ring pattern.) Sometimes adjusting the radius of the pattern is helpful in finding the exact center of the pattern, but the radius does not affect the plot - values are plotted to the farthest corner of the image.
Invoke the Plot Pattern menu. If this is the first plot for the image, the computer will take a little while to build up a radius table.
The averager scans the entire image, taking the sum (and counts) of each pixel versus the distance from the center. The end point of the plot is either for the farthest point in the image from the center, or the farthest non-zero value (for radius) from the center.
Clicking on the plot will show the x (radius) and y (average intensity) values in blue (lower left). The values shown in the figure above were shown after clicking on the plot at the top of the small peak, ie. at the intersection of the black lines at (r, Av). Actually, the plot may be clicked at any height (y) for a given r value.
There may be a blank space in the profile after the plot is clicked. Clicking on the lower right corner (the grow box) will redraw the plot. The plot will be resized with the window if the grow box is moved.
List the values (x in pixels, average intensity value) to a file with the Print Profile menu. If the same file name is used, the file will be overwritten. First collumn is the index or radius value of the plot in pixels, and the second is the (averaged) intensity value.
The following is the first part of the printout - the first collumn is the index, which corresponds to the radius. Idx = R = 0 corresponds to the central pixel, of which there is only one. (The location of the center is constrained to be at the center of a pixel). Next followages the average of the intensity values around the ring of that radius, the number of pixels in the ring, the sum or total of all of the intensity values, and the relative standard deviation of the intensity values. The relative standard deviation is the standard deviation divided by the average.

Idx  Average Count      Tot    Sigma
  0    151.00     1      151     0.00
  1    146.62     8     1173     0.03
  2    148.37    16     2374     0.12
  3    143.80    20     2876     0.13
  4    133.67    24     3208     0.17
  5    128.70    40     5148     0.17
  6    127.92    36     4605     0.17
  7    131.15    48     6295     0.19
  8    132.37    56     7413     0.19
  9    131.52    56     7365     0.21
 10    133.19    68     9057     0.18
 11    134.25    64     8592     0.16
 12    131.87    80    10550     0.16
 13    127.37    92    11718     0.16
 14    123.23    88    10844     0.19
 15    122.32    96    11743     0.18
...